With regard to other kids taking toys, I am surprised that the other parents don't make their kids return the toys. Nonetheless, when I'm in situations where I feel like a parent needs to get involved and other parents are either not around or not stepping in, I almost always step in myself. I figure that I would want someone else to tell my kid to give the toy back, not to hit, to share, etc. if I weren't there to do it. I want my kids to learn that the rules apply even when Mommy isn't watching. I do not in fact know whether other parents approve of my intervention, but I guess I've decided that I don't care that much (although I always feel awkward about instructing someone else's kids) because ultimately I want my own children to learn the rules. At such a young age, I don't think it's fair to expect kids to always be able to stick up for themselves or negotiate situations, so I wouldn't worry about teaching your daughter to depend on you too much right now (when she gets a little older, though, I do think she will need to learn how to take over herself if it hasn't happened naturally). For example, I have taught my 3-year-old to say "excuse me" when he wants to get by another child (say, when they are playing around a train table) instead of pushing his way through, and he's very good about that now. But the other child usually doesn't pay any attention and doesn't move. I don't want my son to conclude that pushing is more effective than saying "excuse me," so as soon as he says it I intervene to ask the other child to please let him by (except in rare circumstances when the child does actually move).
As for the shyness, my 3-year-old is nervous about social situations as well, and I was also a shy kid. I do not have him in daycare or preschool, but I do try to take him to library story times, gym class, and things like that. Gym class in particular has really boosted his self-confidence (we use The Little Gym, but I am sure it totally depends on the instructors). If you decide to take your daughter out of daycare, you can probably find activities (free and otherwise) through local libraries, rec departments, or parents groups to allow you to give her social experience.
Good luck!